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arXiv · 2403.02881

The elephant random walk in the triangular array setting

Rahul Roy·Masato Takei·Hideki Tanemura
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Abstract

Gut and Stadm\"{u}ller (2021, 2022) initiated the study of the elephant random walk with limited memory. Aguech and El Machkouri (2024) published a paper in which they discuss an extension of results by Gut and Stadtm\"{u}ller (2022) for an "increasing memory" version of the elephant random walk without stops. Here we present a formal definition of the process which has been hinted at Eq. (2.2) in Gut and Stadtm\"{u}ller (2022). This definition is based on the triangular array setting. We give a positive answer to the open problem in Gut and Stadtm\"{u}ller (2022) for the elephant random walk, possibly with stops. We also obtain the CLT for the supercritical case of this model.

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Rahul Roy, Masato Takei, Hideki Tanemura. 2024-03-05. The elephant random walk in the triangular array setting. https://doi.org/10.1017/jpr.2024.106

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